[discia] GCSE Maths › Geometry & Measures › Faces, Edges and Vertices

Faces, Edges and Vertices

discia.org 10 questions · 29 marks
Name Date
  1. Either paper 3 marks

    Think about a hexagonal prism.

    (a)

    How many faces does it have?

    (b)

    How many edges does it have?

    (c)

    How many vertices does it have?

    Show answer
    (a) \(8\)
    (b) \(18\)
    (c) \(12\)
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  2. Either paper 3 marks

    A traffic cone is a cone.

    (A face is flat. A curved surface is not flat, so it is described separately. An edge is where two surfaces meet.)

    (a)

    How many flat faces does it have?

    (b)

    How many curved surfaces does it have?

    (c)

    How many edges does it have?

    Show answer
    (a) \(1\)
    (b) \(1\)
    (c) \(1\)
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  3. Either paper 1 mark

    Which of these is a correct statement about this solid?

    Tick one.

    - It has 8 edges. - It has 8 faces. - It has 8 planes. - It has 8 vertices.

    Show answer
    It has 8 vertices.
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  4. Either paper 3 marks

    Here are five solids. Dashed lines show edges you cannot see from this side.

    triangular-based pyramid cuboid pentagonal prism triangular prism cylinder
    (a)

    How many faces does the cuboid have?

    (b)

    How many edges does the pentagonal prism have?

    (c)

    How many faces does the triangular prism have?

    Show answer
    (a) \(6\)
    (b) \(15\)
    (c) \(5\)
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  5. Either paper 2 marks

    A solid has \(5\) faces, \(8\) edges and \(5\) vertices, and four triangles meet at a point above a square.

    Write down the name of the solid.

    Show answer
    square-based pyramid
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  6. Either paper 4 marks

    The diagram shows a cuboid. The dashed lines are the edges you cannot see from this side.

    7 cm2 cm6 cm
    (a)

    State the number of faces.

    (b)

    State the number of edges.

    (c)

    State the number of vertices.

    (d)

    Find the volume of the cuboid.

    Show answer
    (a) \(6\)
    (b) \(12\)
    (c) \(8\)
    (d) \(84\ \text{cm³}\)
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  7. Either paper 5 marks

    The diagram shows a triangular prism.

    8 cm6 cm13 cm
    (a)

    State the number of faces.

    (b)

    State the number of edges.

    (c)

    State the number of vertices.

    (d)

    Find the volume of the prism.

    Show answer
    (a) \(5\)
    (b) \(9\)
    (c) \(6\)
    (d) \(312\ \text{cm³}\)
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  8. Either paper 2 marks

    A pyramid has \(7\) faces and \(12\) edges.

    Euler's formula for a solid with flat faces is \(F + V - E = 2\).

    Use it to work out how many vertices the pyramid has.

    Show answer
    \(7\)
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  9. Either paper 3 marks

    Think about a hexagonal prism.

    (a)

    How many faces does it have?

    (b)

    How many edges does it have?

    (c)

    How many vertices does it have?

    Show answer
    (a) \(8\)
    (b) \(18\)
    (c) \(12\)
    Another like this
  10. Either paper 3 marks

    A tin of soup is a cylinder.

    (A face is flat. A curved surface is not flat, so it is described separately. An edge is where two surfaces meet.)

    (a)

    How many flat faces does it have?

    (b)

    How many curved surfaces does it have?

    (c)

    How many edges does it have?

    Show answer
    (a) \(2\)
    (b) \(1\)
    (c) \(2\)
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discia.org Faces, Edges and Vertices · sheet 1
Answers Faces, Edges and Vertices · sheet 1
  1. (a) \(8\)
    (b) \(18\)
    (c) \(12\)
  2. (a) \(1\)
    (b) \(1\)
    (c) \(1\)
  3. It has 8 vertices.
  4. (a) \(6\)
    (b) \(15\)
    (c) \(5\)
  5. square-based pyramid
  6. (a) \(6\)
    (b) \(12\)
    (c) \(8\)
    (d) \(84\ \text{cm³}\)
  7. (a) \(5\)
    (b) \(9\)
    (c) \(6\)
    (d) \(312\ \text{cm³}\)
  8. \(7\)
  9. (a) \(8\)
    (b) \(18\)
    (c) \(12\)
  10. (a) \(2\)
    (b) \(1\)
    (c) \(2\)
discia.org Faces, Edges and Vertices · sheet 1